Ce travail de thèse porte sur l'extension et l'analyse d'un solveur volumes finis eulérien, co-localisé avec capture d'interfaces pour la simulation des écoulements multi-matériaux non miscibles. Les extensions proposées s'inscrivent dans la volonté d'élaborer un outil de simulation multi-physiques. Dans le cadre de ce mémoire, le caractère multi-physiques recouvre les champs que nous allons détailler. Nous traitons le cas des écoulements radiatifs modélisés par un système à deux températures qui couple les phénomènes purement hydrodynamiques aux phénomènes radiatifs. Nous proposons un solveur permettant la prise en compte des effets de tension superficielle à l'interface entre deux fluides. Nous développons un solveur implicite permettant la simulation précise d'écoulements faisant intervenir de faibles nombres de Mach par le biais d'une méthode de renormalisation de la diffusion numérique. Enfin, les effets tri-dimensionnels sont considérés ainsi que la possibilité d'étendre le schéma de base aux écoulements à un nombre quelconque de matériaux. A chaque étape, les solveurs développés sont validés sur des cas-tests. / This work is devoted to the extension of a eulerian cell-centered finite volume scheme with interfaces capturing for the simulation of multimaterial fluid flows. Our purpose is to develop a simulation tool which could be able to handle multi-physics problems in the following sense. We address the case of radiating flows, modeled by a two temperature system of equations where the hydrodynamics are coupled to radiation transport. We address a numerical scheme for taking surface tension forces into account. An implicit scheme is proposed to handle low Mach number fluid flows by means of a renormalization of the numerical diffusion. Eventually, the scheme is extended to three-dimensional flows and to multimaterial flows, that is with an arbitrary number of materials. At each step, numerical simulations validate our schemes.

Cette thèse est consacrée à l’analyse mathématique de trois problèmes d’écoulements de fluides viscoélastiques de type Oldroyd. Tout d’abord, nous étudions des écoulements stationnaires faiblement compressibles dans un domaine borné avec des conditions au bord de type "rentrante-sortante". Nous étudions aussi le problème d’écoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une méthode de point fixe (premier et deuxième problèmes) et une décomposition de Helmoltz (deuxième problème), nous montrons des résultats d’existence et d’unicité des solutions. Nous étudions également le cas d’un écoulement non stationnaire. Nous montrons un résultat d’existence locale et un résultat d’existence globale, avec des conditions initiales suffisamment petites, pour des fluides compressibles. Nous démontrons aussi la convergence du modèle d’écoulement viscoélastique compressible à faible nombre de Mach vers le modèle incompressible lorsque les données initiales sont "bien préparées" / In this PHD thesis, we study three problems for viscoelastic flows of Oldroyd type. First, we study steady flows of slightly compressible in a bounded domain with non-zero velocities on the boundary ; the pressure and the extra-stress tensor are prescribed on the part of the boundary corresponding to entering velocity. This causes a weak singularity in the solution at the junction of incoming and outgoing flows. We also study the problem of steady flows of slightly compressible fluids with zero boundary conditions in a domain with an isolated corner point. Using a method of fixed point (first and second problems) and a Helmoltz decomposition (second problem), we show some results of existence and uniqueness of solutions. In the last part, we study the case of a non-steady flow : we show some results of local and of global existence, with sufficiently small initial data, for compressible flows. The zero-Mach number limit is also established

Le modèle numérique que nous avons développé au cours de cette thèse présente deux caractéristiques principales : un modèle dilatable pour l'eau et la prise en compte de domaines ouverts. Les difficultés associées au premier aspect concernent l'adaptation de la loi d'état de l’eau au modèle dilatable sous l’approximation à faibles nombres de Mach, tandis que celles associées au second sont relatives à la mise en œuvre de conditions aux limites numériques de sortie compatibles avec l'algorithme de projection utilisé. Les résultats de simulations d'écoulement de convection mixte en canal horizontal chauffé par le bas ont été confrontés à celles utilisant l'approximation de Boussinesq et aux expériences. / The 3D numerical model which we developed in this thesis presents two main features: a Low-Mach-Number approximation for water along with an open boundary condition formulation. Indeed, the difficulties related to the former point stand in a computationally efficient adaptation of the water equation of state in the framework of Low Mach number approximation, whereas the difficulties related to the latter concern the introduction of Open Boundary Conditions in the projection algorithm used. We have computed a mixed convection flow in a horizontal channel uniformly heated from below and compared the results obtained with both the Boussinesq approximation and experimental results.

Dans cette thèse on s'intéresse aux jets en écoulement transverse dans une configuration générique de celle du refroidissement par effusion de chambres de combustion aéronautiques. L'amélioration des modèles de paroi avec transfert de masse passe par une meilleure connaissance de l'interaction entre les jets et l’écoulement principal. Nous avons donc réalisé la simulation numérique directe d'un jet issu d'un perçage incliné avec ou sans giration, pour des écoulements isothermes, turbulents et à bas nombre de Mach, dans un contexte compressible. Pour cela nous avons travaillé avec la bibliothèque AeroSol d'éléments finis continus et discontinus sur maillage hybride. En particulier nous nous sommes intéressés à la stabilité des flux numériques pour le compressible instationnaire associés à la méthode de Galerkin discontinue lorsque le nombre de Mach tend vers zéro. Nous avons pu mettre en évidence des comportements instables lors de l'utilisation de discrétisation temporelle explicite que nous avons corrigés en proposant un nouveau flux. Dans un deuxième temps, nous avons effectué les développements nécessaires à la réalisation des calculs. Nous nous sommes en particulier intéressés à la génération d'un champ de vitesse turbulent synthétique par la méthode SEM (Synthetic Eddy Method) que nous avons implantée dans AeroSol et validée. Grâce aux outils de post-traitement développés, nous avons conduit l'analyse de nos résultats. Dans le cas sans giration, les comparaisons avec les résultats expérimentaux et les résultats de simulations RANS que nous avons obtenus en parallèle sur la configuration du banc d'essai MAVERIC sont encourageants. La structure moyenne d'ensemble du jet est notamment correctement reproduite. En ce qui concerne la cas avec giration, le comportement attendu de déflexion successive du jet dans les deux plans caractéristiques (plan d'injection et plan de l'écoulement transverse) est bien reproduit et illustre tout le potentiel prévisionnel de la librairie de calcul que nous avons contribué à développer. / In this work we are interested in jet in crossflow in a generic configuration to the one used in effusion cooling for combustion chambers. Improved wall models with mass transfer requires a better knowledge of the interaction between the jets and the main flow. We therefore carried out the direct numerical simulation of a jet issuing from an inclined hole with or without gyration, for isothermal turbulent flow at low Mach number, in a compressible context. To achieved this, we worked with the continuous and discontinuous finite element library : AeroSol on hybrid grid. In particular we studied the stability of numerical flux for the unsteady compressible flow associated with discontinuous Galerkin method when the Mach number tends to zero. We were able to demonstrate unstable behavior when using explicit time discretization and we corrected them by providing a new flux. In a second time, we have performed the necessary development to achieve the calculations. We have been especially interested in the generation of a synthetic turbulent velocity field using the SEM method (Synthetic Eddy Method) that we have implemented in aerosol and validate. Thanks to the developed post-processing tools, we have conducted an analysis of our results. In the case without gyration, comparisons with experimental results and the results of RANS simulations we obtained on the Maveric test-bench configuration are encouraging. The mean flow of the jet is correctly reproduced. In the case with gyration, the expected behavior of successive deflection of the jet in both planes (injection plane and transverse plane of the flow) is reproduced and shows all the potential of the AeroSol library we helped to develop.

Este trabalho relata um estudo numÃrico das caracterÃsticas Ãpticas de um interferÃmetro Mach-Zehnder disposto em uma configuraÃÃo com quatro estÃgios e um ressonador Ãptico em anel. O interferÃmetro Mach-Zehnder foi construÃdo numa versÃo com fibra comum e outra com fibra de dispersÃo decrescente considerando um perfil de dispersÃo linear. O ressonador Ãptico em anel foi constuÃdo com um guia de onda cujo o Ãndice de refraÃÃo nÃo linear foi moldado com um perfil linear crescente. A transmissÃo e o fator de compressÃo dos pulsos de saÃda sÃo analisados nos regimes de soliton e quasi-soliton para ambos os dispositivos. Os resultados mostraram que a transmissÃo do interferÃmetro Mach-Zehnder à fortemente dependente da potÃncia de entrada em ambos os regimes. O nÃvel de crosstalk tambÃm à dependente da potÃncia de entrada e da dispersÃo da fibra. Para potÃncias de entrada altas, o nÃvel de crosstalk à mais baixo para o dispositivo com fibra de dispersÃo decrescente no regime de soliton. Para esta configuraÃÃo, o nÃvel de crosstalk mÃnimo encontrado (-22 dB) foi para a potÃncia normalizada de entrada P = 2,7. No regime de quasi-soliton, em geral, o nÃvel de crosstalk mÃnimo à mais baixo para o interferÃmetro Mach-Zehnder com fibra de dispersÃo decrescente em potÃncias de entrada altas, mas com a possibilidade de se obter um nÃvel de crosstalk menor para o dispositivo utilizando fibra comum. A razÃo de extinÃÃo à tambÃm muito dependente da potÃncia de entrada e sofre degeneraÃÃo quando a potÃncia de entrada aumenta. Para potÃncias de entrada baixas, o interferÃmetro Mach-Zehnder apresenta uma razÃo de extinÃÃo melhor em potÃncias de entrada mais altas no regime de soliton. No regime de quasi-soliton, a melhor razÃo de extinÃÃo à obtida para o interferÃmetro Mach-Zehnder com fibra comum em potÃncias de entrada altas. Pode-se dizer que a operaÃÃo do dispositivo como uma chave Ãptica nÃo melhora com o uso de fibra de dispersÃo decrescente. Entretanto, para operaÃÃo de multiplex/demultiplex, o interferÃmetro Mach-Zehnder construÃdo com fibra de dispersÃo decrescente mostrou melhoramentos no nÃvel de crosstalk no regime de soliton e, dependendo da potÃncia de entrada, tambÃm no regime de quasi-soliton. No estudo do ressonador Ãptico em anel foi encontrado que a perda do guia de onda que forma a cavidade anelar diminui a transmissÃo em ambos os regimes, mas mantÃm o mesmo comportamento nÃo linear. O uso de um Ãndice de refraÃÃo nÃo linear com um perfil linear crescente leva à compressÃo ou alargamento temporal, dependendo da potÃncia de entrada, no regime de soliton. No regime de quasi-soliton nÃo foi observado deformaÃÃo temporal dos pulsos de saÃda. Isto indica que, em mÃdia, os pulsos de saÃda estÃo com a mesma duraÃÃo temporal que os pulsos de entrada. Os resultados tambÃm mostraram que hà um aumento da transmissÃo quando um Ãndice de refraÃÃo nÃo linear com um perfil linear crescente à usado. Assim, o decrÃscimo na transmissÃo associado à perda do guia de onda pode ser evitado. As caracterÃsticas de transmissÃo e a forma dos pulsos Ãpticos de saÃda do interferÃmetro Mach-Zehnder e do ressonador Ãptico em anel serÃo de interesse em circuitos Ãpticos e sistemas de comunicaÃÃes totalmente Ãpticos no futuro.

Les calculs d'écoulements stationnaires peuvent être considérés comme efficace si l?état stationnaire est atteint pour un temps CPU réduit mais aussi si la place mémoire utilisée reste faible; cette dernière exigence devient primordiale pour les applications industrielles où le nombre de points de calcul est très important. Ceci vaut également pour les écoulements instationnaires, désormais classiquement résolus via une approche pas-de-temps dual pour laquelle les états physiques successifs sont vus comme des états stationnaires vis-à-vis d'un temps fictif. Le besoin crucial de méthodes implicites à faible encombrement mémoire a conduit au développement de traitements sans matrice. Pour les applications qui intéressent le CEA, à savoir la simulation d'écoulements réactifs multi-espèces à l'intérieur d'une enceinte de réacteur nucléaire à eau pressurisée, les méthodes doivent être assez versatiles pour traiter la gamme d'écoulements allant du quasi-incompressible au fortement compressible. Le préconditionnement bas-Mach des équations de Navier-Stokes permet d'appliquer en régime incompressible les schémas initialement conçus pour la simulation des écoulements compressibles. Le présent travail montre comment obtenir un traitement implicite sans matrice pour tout régime d'écoulement lorsque la phase implicite contient une matrice de préconditionnement; l'efficacité intrinsèque du schéma implicite sans matrice couplé à une technique de relaxation de type Jacobi par point (PJ) ou Symmetric Gauss-Seidel (SGS) est étudiée grâce à une analyse de Von Neumann; puis des comparaisons avec des méthodes implicites blocs standards sont effectuées. La méthode implicite sans matrice est finalement implémentée au sein du code non-structuré CAST3M et elle est appliquée à la modélisation d'un Té de mélange à faible nombre de Mach. Le schéma implicite sans matrice constitue une alternative compétitive pour la simulation des écoulements compressibles et faiblement compressibles en maillages non-structurés.

One of the major technological innovations that are necessary for faster and cheaper access-to-space will be the commercial realization of supersonic combustion jet engines (SCRAMJET). The establishment of the flow through the inlet is one the prime requirement for the success of a SCRAMJET engine. The flow through a SCRAMJET inlet is dominated by inviscid /viscous coupling, transition, shock-shock interaction, shock boundary layer interaction, blunt leading edge effects and flow profile effects. Although the literature is exhaustive on various aspects of flow features associated with SCRAMJET engines, very little is known on the fundamental gasdynamic features dictating the flow establishment in the SCRAMJET inlet. On one hand we need the reduction of flight Mach number to manageable supersonic values inside the SCRAMJET combustor, but on the other hand we have to achieve this with minimum total pressure loss. Hence the dynamics of ramp/cowl shock interaction process ahead of the inlet has a direct bearing on the quality and type of flow inside the SCRAMJET engine. There is virtually no data base in the open literature focusing specifically on the cowl/ramp shock interactions at hypersonic Mach numbers. Hence in this backdrop, the main aim of the present investigation is to systematically understand the ramp/cowl shock interaction processes in front of a generic inlet model. Since we are primarily concerned with the shock interaction process ahead of the cowl all the investigations are carried out without any fuel injection. Variable geometry is necessary if we want to operate the inlet for a wide range of Mach numbers in actual flight. The investigation mainly comprises of three variable geometry configurations; namely, variation of contraction ratios at 00 cowl (CR 8.4, 5.0 and 4.3), variation of cowl length for a given chamber height (four lengths of cowls at 10 mm chamber height) and variation of cowl angle (three angles cowl each for two chamber heights). The change in cowl configuration results in different ramp/cowl shock interaction processes affecting the performance of the inlet. Experiments are performed in IISc hypersonic shock tunnel HST 2 (test time ~ 1 ms) at two nominal Mach numbers 8.0 and 5.74 for design and off-design testing conditions. Exhaustive numerical simulations are also performed to compliment the experiments. Further the effect of concentrated energy deposition on forebody /cowl shock interactions has also been investigated. A 2D, planar, single ramp scramjet inlet model has been designed and fabricated along with various cowl geometries and tested in a hypersonic shock tunnel to characterize the forebody/cowl shock interaction process for different inlet configurations. Further a DC plasma power unit and a plasma torch have been designed, developed and fabricated to serve as energy source for conducting flow-alteration experiments in the inlet model. The V-I characteristics of the plasma torch is studied and an estimation of plasma temperature is also performed as a part of characterizing the plasma flame. Initial standardization experiments of blunt body flow field alteration using the plasma torch and hence its drag reduction, are performed to check the torch’s suitability to be used as a flow-altering device in a shock tunnel. The plasma torch is integrated successfully with the inlet model in a shock tunnel to perform experiments with plasma jet as the energy source. The above experiments are first of its kind to be conducted in a shock tunnel. They are performed at various pressure ratios and supply currents. Time resolved schlieren flow visualization using Phantom 7.1 (Ms Vision Research USA) high speed camera, surface static pressure measurements inside a generic inlet using miniature kulite transducer and surface convective heat transfer rate measurements inside a generic inlet using platinum thin film sensors deposited on Macor substrate are some of the shock tunnel flow diagnostics that have been used in this study. Some of the important conclusions from the study are: • Experiments performed at different contraction ratios show different shock patterns. At CR 8.4, the SOL condition is satisfied, but the flow gets choked due to over contraction and flow through inlet is not established. For CR 5.0, formation of a small Mach stem before the chamber is observed with the reflection point on the cowl and the weak reflected shock entering inside the chamber. The Mach stem grows with time. For CR 4.3, the forebody/cowl shock interference created an Edney’s Type II shock interaction pattern. However, at off-design conditions, for CR 5 the shock reflection is regular and at CR 4.3, the Edney’s Type II pattern lasts for a short time. • For all lengths of cowl tested, 131mm and 141mm showed Edney’s Type II shock interference where as 151mm showed Edney’s Type I pattern at design condition. In all cases the flow is choked for high contraction ratio. At off-design condition these shock patterns do not last for the entire test time but rather it becomes a lambda pattern with the normal shock before the inlet. • For inlet configurations with cowl angle other than 00, the flow is found to be established for all cases at designed condition and except for 100 cowl at off-design condition. • For CR 8.4 the peak value of pressure (~1.7x104 Pa) occurs at a location of 151mm, where as for CR 5.0 and 4.3 they occur at 188mm and 206mm having values ~1.6x104 Pa and ~1.4x104 Pa respectively. These locations indicate the likely locations of shock impingements inside the chamber. • For cowl angle of 00 for a 10 mm chamber the maximum pressure value recorded is ~1.7x104 Pa whereas for 100 and 200 cowl it is ~1.1x104 Pa and 1.2 x104 Pa respectively. This is because in the first case the inlet is choked because of over contraction whereas in the other two cases the CR is less and flow is established inside the inlet. • The average heat transfer rates of last four heat transfer gauges (180 mm, 190 mm, 200 mm and 210 mm from the forebody tip) for all lengths of cowls tested are found to be almost same (~ 20 W/cm2). This is because the flow is choked in all these cases. The numerical simulation also shows uniform distribution here, consistent with the experimental findings. • The locations of heat transfer peaks for 100 cowl at design condition can be observed to be occurring at 170 mm and 200 mm from the forebody tip having values ~44 W/cm2 and ~39 W/cm2 respectively. For a 200 cowl they seem to be occurring at 170 mm and 180 mm from the forebody tip having values ~50 W/cm2 and ~30 W/cm2. These locations indicate the likely locations of shock impingements inside the chamber. With the evolution of concept of upstream fuel injection in recent times these may the most appropriate locations for fuel injection. • At higher jet pressure ratios the plasma jet/ramp shock interaction results in a lambda shock pattern with the triple point forming vertically above the cowl level. This means the normal shock stands in front of the inlet making a part of the flow entering the inlet subsonic. The reflected shock from the triple point also separates the ramp boundary layer. • At lower jet pressure ratios the triple point is formed below the cowl level and the flow entering inside the inlet is supersonic. The reflected shock interacts with the cowl shock and a weak separation shock is seen. • Experiments are performed with concentrated DC electric discharge as energy source. Even though the amount of energy dumped here is less than 0.25% of the total energy it creates a perceptible disturbance in the flow. • Experiments are also performed to see the effect of electric discharge as energy source on height of Mach stem for a given inlet configuration. Deposition of energy in the present location does not seem to alter the Mach stem height. However more experiments need to be performed by varying the energy location to see its effect. Non-intrusive energy sources like microwave and lasers can be thought of as options for depositing energy to study its effect on Mach stem height. Since they provide more flexibility on varying the location of energy the optimum location of energy can be found out for highest reduction of Mach stem height.

Cette thèse est consacrée à l'analyse mathématique de quelques modèles hétérogènes intervenants en mécanique des fluides. En particulier, elle est consacré a l'étude théorique des systèmes d'équations aux derivées partielles décrivants les trois modèles principaux que nous voulons présenter dans la suite. Le premier modèle étudié dans cette thèse est consacré à l'étude de l'écoulement d'un fluide visqueux newtonien et incompressible dans un bassin avec bathymétrie qui dégenère proche du bord. Le modèle mathématique étudié provient alors des équations de Navier-Stokes incompressible. On cherche à montrer que le problème de Cauchy correspondant est bien posé, au sens qu'on peut garantir l'existence globale et l'unicité de solutions faibles. Nous discuterons aussi la régularité de la solution faible. Finalement,nous établissons la convergence de la solution du modèle visqueux vers celle du modèle non visqueux quand le coefficient de viscosité tend vers zéro.La deuxième partie est dédiée à l'étude d'un modèle issu du système de Navier-Stokes dispersif ( il contient une correction dispersive) qui est lui meme obtenu à partir de la théorie cinétique des gaz. Notre modèle mathématique est dérivé a partir de ce dernier en supposant que le nombre de Mach est très faible. Le modèle obtenu est nommé effet fantôme (ou ghost effect an anglais), puisqu'il ne peut pas être obtenu à partir du modèle de Navier-Stokes compressible classique. L'objectif dans ce cadre sera d'étendre un résultat concernant l'existence locale d'une solution forte vers l'existence globale d'une solution faible. L'ingrédient principal dans notre analyse est une nouvelle inégalité fonctionnelle de type Log-Sobolev.La troisième partie de ce document est une contribution à une thématique de recherche se proposant d'analyser la compréhension des phénomènes rencontrés en géophysique qui font intervenir des milieux granulaires. Le modèle mathématique choisi est de type Bingham incompressible dont on fait dépendre le seuil de plasticité et le coe fficient de viscosité de la pression. On montre un résultat d'existence globale d'une solution faible du problème de Cauchy associé. / This thesis is devoted to the mathematical analysis of heterogeneous models raised by fluid mechanics. In particular, it is devoted to the theoretical study of partial differential equations used to describe the three main models that we present below.Initially, we are interested to study the motion of a compressible newtonienfluids in a basin with degenerate topography. The mathematical model studied derives from incompressible Navier-Stokes equations. We are interested to prove that the Cauchy problem associated is well posed. Well-posedness means that there exists a solution, that it is unique. In the meantime, we prove that the solution of the viscous model converges to the one of the inviscid limit model when the viscosity coe cient tends to zero.The second part in my thesis is devoted to study a model that arises from dispersive Navier-Stokes equations (that includes dispersive corrections to the classical compressible Navier-Stokes equations). Our model is derived from the last model assuming that the Mach number is very low. The obtained system is a Ghost eect system, which is so named because it can be derived from Kinetic theory. The main goal of this part is to extend a result concerning the local existence of strong solution to a global-in time existence of weak solutions. The main ingredient in this work is a new functional inequality of Log-Sobolev type.The last part of my thesis is a part of a research theme intends to analyze the understanding of phenomena encountered in geophysics which involves granular media. The mathematical model is of Bingham incompressible type with viscosity and placticity depending on the pressure. We provide a global existence of weak solutions of the Cauchy problem associated.

LIMA, José Luiz Sousa. Estudo do desempenho de filtros ópticos interferométricos: interferômetro Mach-Zehnder de fibra óptica e ressonador óptico em anel. 2006. 96 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2006. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-05-05T20:15:39Z No. of bitstreams: 1 2006_tese_jlslima.pdf: 688113 bytes, checksum: 11efdee52324ab34ae806b2466f4f088 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-05-07T14:27:12Z (GMT) No. of bitstreams: 1 2006_tese_jlslima.pdf: 688113 bytes, checksum: 11efdee52324ab34ae806b2466f4f088 (MD5) / Made available in DSpace on 2015-05-07T14:27:12Z (GMT). No. of bitstreams: 1 2006_tese_jlslima.pdf: 688113 bytes, checksum: 11efdee52324ab34ae806b2466f4f088 (MD5) Previous issue date: 2006

Dans les centrales solaires à tour, le flux solaire est concentré vers un récepteur solaire où son énergie est transférée à un fluide caloporteur. L'écoulement au sein du récepteur solaire est turbulent, fortement anisotherme et à bas nombre de Mach. L'optimisation du récepteur solaire exige une meilleure compréhension et modélisation de l'interaction entre la température et la turbulence. Cette thèse cherche à y contribuer selon deux approches. Tout d'abord, on étudie les échanges énergétiques entre les différentes parties de l'énergie totale. On propose pour cela une nouvelle représentation des échanges énergétiques, fondée sur la moyenne de Reynolds. Cette représentation permet la caractérisation, à partir de simulations numériques directes d'un canal plan bipériodique anisotherme, de l'effet du gradient de température sur les échanges énergétiques associées à l'énergie cinétique turbulente dans les domaines spatial et spectral. Ensuite, on étudie la simulation des grandes échelles des équations de bas nombre de Mach. En utilisant les résultats de simulations numériques directes, on identifie les termes sous-mailles spécifiques à modéliser lorsque l'on utilise le filtre classique, non pondéré, et lorsque l'on utilise le filtre de Favre, pondéré par la masse volumique. Dans les deux cas, on évalue a priori la performance de différents modèles sous-mailles. La pertinence des modèles est vérifiée a posteriori par la réalisation de simulation des grandes échelles. / In solar power towers, the solar flux is concentrated towards a solar receiver, wherethrough its energy is transferred to a heat transfer fluid. The flow in the solar receiver is turbulent, strongly anisothermal and at low Mach number. The optimisation of the solar receiver requires a better understanding and modelling of the interaction between temperature and turbulence. In this thesis, this is investigated following two approaches. First, we study the energy exchanges between the different parts of total energy. To this end, a new representation of the energy exchanges, based on the Reynolds averaging, is established. The representation allows the characterisation, from direct numerical simulations of a strongly anisothermal channel flow, of the effect of the temperature gradient on the energy exchanges associated with turbulence kinetic energy in the spatial and spectral domains. Second, we study the large-eddy simulation of the low Mach number equations. Using the results of direct numerical simulations, we identify the specific subgrid terms to model when the unweighted classical filter is used and when the density-weighted Favre filter is used. In both cases, the performance of different subgrid-scale models is assessed a priori. The relevance of the subgrid-scale models is then verified a posteriori by carrying out large-eddy simulations.